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# What is greatest positive integer n such that 2^n is a factor of 12^10

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Intern
Joined: 27 Sep 2011
Posts: 14
What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]

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26 Oct 2011, 23:06
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What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60
[Reveal] Spoiler: OA

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Joined: 21 Aug 2010
Posts: 186
Location: United States
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]

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26 Oct 2011, 23:32
1
KUDOS
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

The given number is 12^10
=(2*2*3)^10
=(2^20)*(3^10)

So the greatest possible value for n such that 2^n can be factor of given number is 20.

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]

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27 Oct 2011, 04:02
2
KUDOS
Expert's post
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Please show me the easy way to solve such question...

$$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$
The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20.

Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12!
Try this one.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 27 Sep 2011 Posts: 14 Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] ### Show Tags 27 Oct 2011, 07:03 VeritasPrepKarishma wrote: aselfmademan wrote: What is greatest positive integer n such that 2^n is a factor of 12^10? a)10 b)12 c)16 d)20 e)60 Please show me the easy way to solve such question... $$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$ The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20. Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12! Try this one. Thank you very much.......... I am very weak in this type of PS math Could you please explain 12! math you have given ? _________________ All I want to be A Self-made Man Manager Joined: 21 Aug 2010 Posts: 186 Location: United States GMAT 1: 700 Q49 V35 Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] ### Show Tags 27 Oct 2011, 19:32 VeritasPrepKarishma wrote: aselfmademan wrote: What is greatest positive integer n such that 2^n is a factor of 12^10? a)10 b)12 c)16 d)20 e)60 Please show me the easy way to solve such question... $$12^{10} = (2^2*3)^{10} = 2^{20}*3^{10}$$ The greatest value of n such that $$2^n$$ is a factor of $$12^{10}$$ is 20. Such questions are more popular and a little more complex with factorials. e.g. What is greatest positive integer n such that $$2^n$$ is a factor of 12! Try this one. n = 10 I just counted the number of 2s till 12 since the 12! is multiplication of all numbers till 12 Do you have any faster method which can be used for bigger factorials? _________________ ------------------------------------- Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7960 Location: Pune, India Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink] ### Show Tags 27 Oct 2011, 19:39 2 This post received KUDOS Expert's post Check out this post: http://www.veritasprep.com/blog/2011/06 ... actorials/ It discusses how to solve such questions quickly. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]

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07 Mar 2016, 08:36
What is greatest positive integer n such that 2^n is a factor of 12^10?

a)10
b)12
c)16
d)20
e)60

Similar question to practice: what-is-the-largest-integer-n-such-that-2-n-is-a-factor-of-158297.html
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]

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14 Mar 2016, 04:57
Nice One.
Here breaking down 12^10 => 2^20 *3^10
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Re: What is greatest positive integer n such that 2^n is a factor of 12^10 [#permalink]

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02 Feb 2018, 10:28
Hi All,

This question comes down to exponent rules and how to 'rewrite' a number raised to a power.

12 = (2)(2)(3)

12^2 = (2^2)(2^2)(3^2) = (2^4)(3^2)
12^3 = (2^3)(2^3)(3^3) = (2^6)(3^3)

Seeing this pattern, you should be able to rewrite 12^10...

12^10 = (2^10)(2^10)(3^10) = (2^20)(3^10)

So the largest 'power of 2' that is a factor of 12^10 is 20.

[Reveal] Spoiler:
D

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Re: What is greatest positive integer n such that 2^n is a factor of 12^10   [#permalink] 02 Feb 2018, 10:28
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